# picos.expressions.exp_sumxtr¶

Implements SumExtremes.

## Outline¶

### Classes¶

 SumExtremes Sum of the largest or smallest elements or eigenvalues.

## Classes¶

### SumExtremes¶

class picos.expressions.exp_sumxtr.SumExtremes(**kwargs)[source]

Sum of the largest or smallest elements or eigenvalues.

Definition

Let .

1. If is an -dimensional real vector or matrix and eigenvalues == False, then this is the sum of the largest or smallest scalar elements of , depending on the truth value of largest.

Special cases:

• If , this is either the largest element or the smallest element of .

• If , this is the sum of all elements of .

2. If is an hermitian matrix and eigenvalues == True, then this is the sum of the largest or smallest eigenvalues of , depending on the truth value of largest. Recall that the eigenvalues of a hermitian matrix are real.

Special cases:

• If , this is either the largest eigenvalue or the smallest eigenvalue of .

• If , this equals the trace .

If the given exceeds the of either case, then is silently clipped to .

__init__(x, k, largest, eigenvalues=False)[source]

Construct a SumExtremes.

Parameters
• x (ComplexAffineExpression) – The affine expression to take a sum over.

• k (int) – Number of summands.

• largest (bool) – Whether to sum over the largest (eigen)values as opposed to the smallest.

• eigenvalues (bool) – Whether to sum eigenvalues instead of elements.

property eigenvalues

Whether the sum concerns eigenvalues as opposed to elements.

property full

Whether the sum concerns all (eigen)values of the expression.

property k

Number of (eigen)values to sum.

property largest

Whether the sum concerns largest values as opposed to smallest.

property x

The expression under the sum.